Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms

In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension and diameter for the current fastest routing algorithms, including contraction hierarchies, transit node routing, and hub labeling. In this paper, we show corresponding lower bounds for the same three algorithms. We also show how to improve a result by Milosavljevic which lower bounds the number of shortcuts added in the preprocessing stage for contraction hierarchies. We relax the assumption of an optimal contraction order (which is NP-hard to compute), allowing the result to be applicable to real-world instances. Finally, we give a proof that optimal preprocessing for hub labeling is NP-hard. Hardness of optimal preprocessing is known for most routing algorithms, and was suspected to be true for hub labeling

Supertubes

It is shown that a IIA superstring carrying D0-brane charge can be `blown-up', in a {\it Minkowski vacuum} background, to a (1/4)-supersymmetric tubular D2-brane, supported against collapse by the angular momentum generated by crossed electric and magnetic Born-Infeld fields. This `supertube' can be viewed as a worldvolume realization of the sigma-model Q-lump.Comment: Revision includes mention of some configurations dual to the supertub

The Long Term Optical Variability of the BL Lac object S5 0716+714: Evidence for a Precessing Jet

We present the historic light curve of the BL Lac object S5 0716+714, spanning the time interval from 1953 to 2003, built using Asiago archive plates and our recent CCD observations, together with literature data. The source shows an evident long term variability, over which well known short term variations are superposed. In particular, in the period from 1961 to 1983 the mean brightness of S5 0716+714 remained significantly fainter than that observed after 1994. Assuming a constant variation rate of the mean magnitude we can estimate a value of about 0.11 magnitude/year. The simultaneous occurrence of decreasing ejection velocities of superluminal moving components in the jet reported by Bach et al. (2005) suggests that both phenomena are related to the change of the direction of the jet to the line of sight from about 5 to 0.7 degrees for an approximately constant bulk Lorentz factor of about 12. A simple explanation is that of a precessing relativistic jet, which should presently be close to the smallest orientation angle. One can therefore expect in the next ten years a decrease of the mean brightness of about 1 magnitude.Comment: to appear on The Astronomical Journal, 17 pages, 7 figures. Fig.2 is given as a separated jpg fil

An Index Theorem for Domain Walls in Supersymmetric Gauge Theories

The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain wall has 2(N-1) zero modes, which can be interpreted as the positions and phases of (N-1) constituent domain walls. This implies the existence of moduli for a D-string interpolating between N D5-branes in IIB string theory.Comment: 9 pages, REVTeX4; v2: reference adde

Coexistence of excited states in confined Ising systems

Using the density-matrix renormalization-group method we study the two-dimensional Ising model in strip geometry. This renormalization scheme enables us to consider the system up to the size 300 x infinity and study the influence of the bulk magnetic field on the system at full range of temperature. We have found out the crossover in the behavior of the correlation length on the line of coexistence of the excited states. A detailed study of scaling of this line is performed. Our numerical results support and specify previous conclusions by Abraham, Parry, and Upton based on the related bubble model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been rewritten without including new result

D-brane Solitons in Supersymmetric Sigma-Models

Massive D=4 N=2 supersymmetric sigma models typically admit domain wall (Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution in which a string ends on a wall, and show that it has an effective realization as a BIon of the D=4 super DBI-action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q-lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M-theory as calibrated, or `Q-calibrated', M5-branes in an M-monopole background.Comment: 16 pages, 3 figures, Late

Condensation and interaction range in harmonic boson traps: a variational approach

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the N-T phase diagram is obtained.Comment: 14 pages+4 figures, submitted to phys.rev.

Evidence for Evolving Spheroidals in the Hubble Deep Fields North and South

We investigate the dispersion in the internal colours of faint spheroidals in the HDFs North and South. We find that a remarkably large fraction ~30% of the morphologically classified spheroidals with I<24 mag show strong variations in internal colour, which we take as evidence for recent episodes of star-formation. In most cases these colour variations manifest themselves via the presence of blue cores, an effect of opposite sign to that expected from metallicity gradients. Examining similarly-selected ellipticals in five rich clusters with 0.37<z<0.83 we find a significant lower dispersion in their internal colours. This suggests that the colour inhomogeneities have a strong environmental dependence being weakest in dense environments where spheroidal formation was presumably accelerated at early times. We use the trends defined by the cluster sample to define an empirical model based on a high-redshift of formation and estimate that at z~1 about half the field spheroidals must be undergoing recent episodes of star-formation. Using spectral synthesis models, we construct the time dependence of the density of star-formation. Although the samples are currently small, we find evidence for an increase in $\rho_{SFR}$ between z=0 to z=1. We discuss the implications of this rise in the context of that observed in the similar rise in the abundance of galaxies with irregular morphology. Regardless of whether there is a connection our results provide strong evidence for the continued formation of field spheroidals over 0<z<1.Comment: 13 pages, 11 figures. To appear in MNRAS in response to referee's Report. Figures and paper also available at http://www.ast.cam.ac.uk/~fmenante/HDFs

Resonance Zones and Lobe Volumes for Volume-Preserving Maps

We study exact, volume-preserving diffeomorphisms that have heteroclinic connections between a pair of normally hyperbolic invariant manifolds. We develop a general theory of lobes, showing that the lobe volume is given by an integral of a generating form over the primary intersection, a subset of the heteroclinic orbits. Our definition reproduces the classical action formula in the planar, twist map case. For perturbations from a heteroclinic connection, the lobe volume is shown to reduce, to lowest order, to a suitable integral of a Melnikov function.Comment: ams laTeX, 8 figure

The Moduli Space of BPS Domain Walls

N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler potential to quadrature. In the second part of this paper, we consider semi-local vortices compactified on circle. We argue that, in the presence of a suitable Wilson line, the vortices separate into domain wall constituents. These play the role of fractional instantons in two-dimensional gauge theories and sigma-models.Comment: 16 pages, LaTex, 2 figures; factors of zeta corrected, meaning of cross-terms elucidated, further clarifying comments; (more) references adde